Significant figures calculator (sig figs): counting and rounding rules
Counts the figures of a written value, rounds to n figures, and applies the right rule to a calculation, figures or decimal places.
Result
3
- Reading
- "250." carries 3 significant figures
- Scientific notation
- 2.50e+2
Notes (2)
The ribbon covers the significant figures; the signs in pale ink are not significant.
This writing asserts 3 significant figures, that is a value known to ± 0.5.
Calculation, assumptions and sources
OverviewCounts the significant figures of a written value and gives its implicit uncertainty, rounds a value to n figures, and applies the textbook rule to a calculation: minimum significant figures for × and ÷, least precise decimal place for + and −.
Counts the significant figures of a written value and gives its implicit uncertainty, rounds a value to n figures, and applies the textbook rule to a calculation: minimum significant figures for × and ÷, least precise decimal place for + and −. The count applies to the writing, zeros included: "0.50", "250" and "250." carry 2, 2 and 3 figures.
Method & formulas× and ÷: min(significant figures)
The significant-figures rule applies to × and ÷, the decimal-places rule to + and −.
- Significant figure
- every written digit from the first non-zero one, trailing zeros included when a decimal point is present.
- Leading zeros
- not significant: "0.0034" carries two figures.
- Trailing zeros of an integer
- ambiguous, and not counted by convention; "250." or "2.50e2" assert them.
- Implicit uncertainty
- half the step of the last asserted decimal: "12.3" means 12.3 ± 0.05.
Validity domainThese rules approximate uncertainty propagation: they give an order of magnitude, not an exact interval.
These rules approximate uncertainty propagation: they give an order of magnitude, not an exact interval. When uncertainties are known, uncertainty propagation is preferable. They apply to the final result; intermediate steps keep one or two extra figures. Exact numbers (counts, defining factors such as the 2 in 2πr) do not limit the result; both operands are treated as measurements.